It is well established that the temperature gradients in the interiors of internally-heated mantle convection models are subadiabatic (e.g. Parmentier et al., 1994; Bunge et al., 1997, 2001). The subadiabatic gradients have been explained to arise due to a balance between vertical advection and internal heating, however, a detailed analysis of the energy balance in the subadiabatic regions has not been undertaken. In this research, I examine in detail the energy balance in a suite of two-dimensional convection calculations with mixed internal and basal heating, depth-dependent viscosity and continents. I find that there are three causes of subadiabatic gradients. One is the above-mentioned balance, which becomes significant when the ratio of internal heating to surface heat flux is large. The second mechanism involves the growth of the overshoot (maximum and minimum Temperatures along a geotherm) of the geotherm near the lower boundary where the dominant balance is between vertical and horizontal advection. The latter mechanism is significant even in relatively weakly internally heated calculations. For time-dependent calculations, I find that local secular cooling can be a dominant term in the energy equation and can lead to subadiabaticity. However, it does not show its signature on the shape of the time-averaged geotherm. I also compare the basal heat flux with parameterized calculations based on the temperature drop at the core-mantle boundary, calculated both with and without taking the subadiabatic gradient into account and I find a significantly improved fit with its inclusion.<p> I also explore a wide range of parameter space to investigate the dynamical interaction between effects due to surface boundary conditions representing continental and oceanic lithosphere and the endothermic phase boundary at 660 km-depth in two-dimensional Cartesian coordinate convection calculations. I find that phase boundary induced mantle layering is strongly affected by the wavelength of convective flows and mixed surface boundary conditions strongly increase the horizontal wavelength of convection. My study shows that for mixed cases the effects of the surface boundary conditions dominate the effects of the phase boundary. I show that the calculations with complete continental coverage have the most significantly decoupled lower and upper mantle flows and substantial thermal and mechanical layering. Unlike the free-slip case where the surface heat flux decreases substantially with increasing magnitude of the Clapeyron slope, surface heat flux is shown to be almost independent of the Clapeyron slope for mixed boundary condition cases. Although very different when not layered, models with free and mixed surfaces have very similar planforms with very large aspect ratio flows when run with large magnitudes of the Clapeyron slope. I also calculate the critical boundary layer Rayleigh number as a measure of the thermal resistance of the surface boundary layer. My results show that the thermal resistance in the oceanic and the continental regions of the mixed cases are similar to fully free and no-slip cases, respectively. I find that, even for purely basally heated models, the mantle becomes significantly subadiabatic in the presence of partial continental coverage. This is due to the significant horizontal advection of heat that occurs with very large aspect ratio convection cells.

It is well established that the temperature gradients in the interiors of internally-heated mantle convection models are subadiabatic (e.g. Parmentier et al., 1994; Bunge et al., 1997, 2001). The subadiabatic gradients have been explained to arise due to a balance between vertical advection and internal heating, however, a detailed analysis of the energy balance in the subadiabatic regions has not been undertaken. In this research, I examine in detail the energy balance in a suite of two-dimensional convection calculations with mixed internal and basal heating, depth-dependent viscosity and continents. I find that there are three causes of subadiabatic gradients. One is the above-mentioned balance, which becomes significant when the ratio of internal heating to surface heat flux is large. The second mechanism involves the growth of the overshoot (maximum and minimum Temperatures along a geotherm) of the geotherm near the lower boundary where the dominant balance is between vertical and horizontal advection. The latter mechanism is significant even in relatively weakly internally heated calculations. For time-dependent calculations, I find that local secular cooling can be a dominant term in the energy equation and can lead to subadiabaticity. However, it does not show its signature on the shape of the time-averaged geotherm. I also compare the basal heat flux with parameterized calculations based on the temperature drop at the core-mantle boundary, calculated both with and without taking the subadiabatic gradient into account and I find a significantly improved fit with its inclusion.<p> I also explore a wide range of parameter space to investigate the dynamical interaction between effects due to surface boundary conditions representing continental and oceanic lithosphere and the endothermic phase boundary at 660 km-depth in two-dimensional Cartesian coordinate convection calculations. I find that phase boundary induced mantle layering is strongly affected by the wavelength of convective flows and mixed surface boundary conditions strongly increase the horizontal wavelength of convection. My study shows that for mixed cases the effects of the surface boundary conditions dominate the effects of the phase boundary. I show that the calculations with complete continental coverage have the most significantly decoupled lower and upper mantle flows and substantial thermal and mechanical layering. Unlike the free-slip case where the surface heat flux decreases substantially with increasing magnitude of the Clapeyron slope, surface heat flux is shown to be almost independent of the Clapeyron slope for mixed boundary condition cases. Although very different when not layered, models with free and mixed surfaces have very similar planforms with very large aspect ratio flows when run with large magnitudes of the Clapeyron slope. I also calculate the critical boundary layer Rayleigh number as a measure of the thermal resistance of the surface boundary layer. My results show that the thermal resistance in the oceanic and the continental regions of the mixed cases are similar to fully free and no-slip cases, respectively. I find that, even for purely basally heated models, the mantle becomes significantly subadiabatic in the presence of partial continental coverage. This is due to the significant horizontal advection of heat that occurs with very large aspect ratio convection cells.